{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"bootstrap_homo.ipynb","version":"0.3.2","provenance":[],"collapsed_sections":[]},"kernelspec":{"name":"python3","display_name":"Python 3"},"accelerator":"GPU"},"cells":[{"cell_type":"code","metadata":{"id":"xAYPKSFrG8AF","colab_type":"code","outputId":"65773175-f080-4607-9ec3-327c2cbfb55b","executionInfo":{"status":"ok","timestamp":1557263438131,"user_tz":-60,"elapsed":8821,"user":{"displayName":"Stratis Markou","photoUrl":"","userId":"09754366312766083286"}},"colab":{"base_uri":"https://localhost:8080/","height":258}},"source":["!pip3 install http://download.pytorch.org/whl/cu92/torch-0.4.1-cp36-cp36m-linux_x86_64.whl\n","!pip3 install torchvision\n","!pip3 install GPy\n","import GPy\n","import time\n","import copy\n","import math\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import seaborn as sns\n","import torch\n","import torch.nn as nn\n","import torch.nn.functional as F\n","from torch.autograd import Variable\n","from torch.optim import Optimizer\n","from torch.optim.sgd import SGD\n","\n","from torchvision import datasets, transforms\n","from torchvision.utils import make_grid\n","from tqdm import tqdm, trange\n","from google.colab import files\n","%config InlineBackend.figure_format = 'svg'"],"execution_count":13,"outputs":[{"output_type":"stream","text":["Requirement already satisfied: torch==0.4.1 from http://download.pytorch.org/whl/cu92/torch-0.4.1-cp36-cp36m-linux_x86_64.whl in /usr/local/lib/python3.6/dist-packages (0.4.1)\n","Requirement already satisfied: torchvision in /usr/local/lib/python3.6/dist-packages (0.2.2.post3)\n","Requirement already satisfied: torch in /usr/local/lib/python3.6/dist-packages (from torchvision) (0.4.1)\n","Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from torchvision) (1.16.3)\n","Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from torchvision) (1.12.0)\n","Requirement already satisfied: pillow>=4.1.1 in /usr/local/lib/python3.6/dist-packages (from torchvision) (4.3.0)\n","Requirement already satisfied: olefile in /usr/local/lib/python3.6/dist-packages (from pillow>=4.1.1->torchvision) (0.46)\n","Requirement already satisfied: GPy in /usr/local/lib/python3.6/dist-packages (1.9.6)\n","Requirement already satisfied: scipy>=0.16 in /usr/local/lib/python3.6/dist-packages (from GPy) (1.2.1)\n","Requirement already satisfied: paramz>=0.9.0 in /usr/local/lib/python3.6/dist-packages (from GPy) (0.9.4)\n","Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from GPy) (1.12.0)\n","Requirement already satisfied: numpy>=1.7 in /usr/local/lib/python3.6/dist-packages (from GPy) (1.16.3)\n","Requirement already satisfied: decorator>=4.0.10 in /usr/local/lib/python3.6/dist-packages (from paramz>=0.9.0->GPy) (4.4.0)\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"1-7dNcVmHA3I","colab_type":"code","outputId":"25b7bb65-a369-4821-aea7-61095367ba5a","executionInfo":{"status":"ok","timestamp":1557263438132,"user_tz":-60,"elapsed":8323,"user":{"displayName":"Stratis Markou","photoUrl":"","userId":"09754366312766083286"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["torch.cuda.device(0)\n","torch.cuda.get_device_name(torch.cuda.current_device())"],"execution_count":14,"outputs":[{"output_type":"execute_result","data":{"text/plain":["'Tesla T4'"]},"metadata":{"tags":[]},"execution_count":14}]},{"cell_type":"code","metadata":{"id":"_1S5kt0omQ-N","colab_type":"code","colab":{}},"source":["def to_variable(var=(), cuda=True, volatile=False):\n","    out = []\n","    for v in var:\n","        \n","        if isinstance(v, np.ndarray):\n","            v = torch.from_numpy(v).type(torch.FloatTensor)\n","\n","        if not v.is_cuda and cuda:\n","            v = v.cuda()\n","\n","        if not isinstance(v, Variable):\n","            v = Variable(v, volatile=volatile)\n","\n","        out.append(v)\n","    return out"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"Va8V78eFFsc9","colab_type":"code","colab":{}},"source":["def log_gaussian_loss(output, target, sigma, no_dim):\n","    exponent = -0.5*(target - output)**2/sigma**2\n","    log_coeff = -no_dim*torch.log(sigma)\n","    \n","    return - (log_coeff + exponent).sum()\n","\n","\n","def get_kl_divergence(weights, prior, varpost):\n","    prior_loglik = prior.loglik(weights)\n","    \n","    varpost_loglik = varpost.loglik(weights)\n","    varpost_lik = varpost_loglik.exp()\n","    \n","    return (varpost_lik*(varpost_loglik - prior_loglik)).sum()\n","\n","\n","class gaussian:\n","    def __init__(self, mu, sigma):\n","        self.mu = mu\n","        self.sigma = sigma\n","        \n","    def loglik(self, weights):\n","        exponent = -0.5*(weights - self.mu)**2/self.sigma**2\n","        log_coeff = -0.5*(np.log(2*np.pi) + 2*np.log(self.sigma))\n","        \n","        return (exponent + log_coeff).sum()"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"rPqBGJbPKaxU","colab_type":"code","colab":{}},"source":["class Net(torch.nn.Module):\n","    def __init__(self, n_feature, n_hidden, n_output, init_log_noise, learn_rate):\n","        super(Net, self).__init__()\n","        self.hidden1 = torch.nn.Linear(n_feature, n_hidden)\n","        self.predict = torch.nn.Linear(n_hidden, n_output)\n","        self.log_noise = nn.Parameter(torch.cuda.FloatTensor([init_log_noise]))\n","        \n","        self.loss_func = log_gaussian_loss\n","        self.optimizer = torch.optim.SGD(self.parameters(), lr = learn_rate, weight_decay = 0)\n","        \n","    def forward(self, x):\n","        x = F.relu(self.hidden1(x))\n","        x = self.predict(x)\n","        return x\n","    \n","    def fit(self, x, y):\n","        x, y = to_variable(var=(x, y), cuda=True)\n","        \n","        # reset gradient and total loss\n","        self.optimizer.zero_grad()\n","        \n","        output = self.forward(x)\n","        loss = self.loss_func(output, y, self.log_noise.exp(), 1)\n","        for param in self.hidden1.parameters(): loss += 0.5*(param**2).sum()\n","        loss = loss/x.shape[0]\n","        \n","        loss.backward()\n","        self.optimizer.step()\n","\n","        return loss"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"ym6HBK-s8GnO","colab_type":"code","outputId":"d399a0b2-15b9-43f4-ae53-450befcae0cb","executionInfo":{"status":"ok","timestamp":1557263454939,"user_tz":-60,"elapsed":19946,"user":{"displayName":"Stratis Markou","photoUrl":"","userId":"09754366312766083286"}},"colab":{"base_uri":"https://localhost:8080/","height":1717}},"source":["np.random.seed(2)\n","no_points = 400\n","lengthscale = 1\n","variance = 1.0\n","sig_noise = 0.3\n","x = np.random.uniform(-3, 3, no_points)[:, None]\n","x.sort(axis = 0)\n","\n","\n","k = GPy.kern.RBF(input_dim = 1, variance = variance, lengthscale = lengthscale)\n","C = k.K(x, x) + np.eye(no_points)*sig_noise**2\n","\n","y = np.random.multivariate_normal(np.zeros((no_points)), C)[:, None]\n","y = (y - y.mean())\n","x_train = x[75:325]\n","y_train = y[75:325]\n","\n","x_mean, x_std = x_train.mean(), x_train.var()**0.5\n","y_mean, y_std = y_train.mean(), y_train.var()**0.5\n","\n","x_train = (x_train - x_mean)/x_std\n","y_train = (y_train - y_mean)/y_std\n","\n","\n","nb_epochs, batch_size, nb_train = 1000, len(x_train), len(x_train)\n","\n","fit_loss_train = np.zeros(nb_epochs)\n","best_net, best_loss = None, float('inf')\n","no_nets, nets, losses = 10, [], []\n","\n","for n in range(no_nets):\n","    net = Net(n_feature=1, n_hidden=200, n_output=1, init_log_noise=0, learn_rate=1e-2).cuda()\n","    \n","    sub_idx = np.random.choice(np.arange(0, len(x_train)), size = (int(len(x_train)*0.8),), replace=True)\n","    x_train_sub, y_train_sub = x_train[sub_idx], y_train[sub_idx]\n","    \n","    for i in range(nb_epochs):\n","\n","        loss = net.fit(x_train_sub, y_train_sub)\n","\n","        if i % 100 == 0:\n","            print('Epoch %d' % i, loss.cpu().data.numpy(), torch.exp(net.log_noise).cpu().data.numpy())\n","            \n","    nets.append(copy.deepcopy(net))\n","    "],"execution_count":18,"outputs":[{"output_type":"stream","text":["Epoch 0 1.0049833 [1.0040159]\n","Epoch 100 0.060154855 [0.5954132]\n","Epoch 200 14.184133 [0.59919554]\n","Epoch 300 0.24480693 [0.8576353]\n","Epoch 400 -0.52866566 [0.37393752]\n","Epoch 500 -0.47787154 [0.40755075]\n","Epoch 600 -0.47490203 [0.41380826]\n","Epoch 700 -0.41914618 [0.4492629]\n","Epoch 800 -0.40289947 [0.46263954]\n","Epoch 900 -0.3374153 [0.50529504]\n","Epoch 0 0.70751053 [0.99758744]\n","Epoch 100 -0.0031776237 [0.56398565]\n","Epoch 200 -0.020823516 [0.6670902]\n","Epoch 300 -0.105920754 [0.61797976]\n","Epoch 400 -0.0569145 [0.6584197]\n","Epoch 500 -0.012299709 [0.69591707]\n","Epoch 600 4.873294 [0.36652088]\n","Epoch 700 -0.0149441715 [0.6714553]\n","Epoch 800 -0.6897275 [0.3066578]\n","Epoch 900 -0.6668208 [0.321763]\n","Epoch 0 0.77746433 [0.9987278]\n","Epoch 100 -0.00709919 [0.5599126]\n","Epoch 200 -0.057044256 [0.6313224]\n","Epoch 300 0.085026145 [0.7507361]\n","Epoch 400 -0.5814239 [0.33509257]\n","Epoch 500 -0.5787069 [0.34140405]\n","Epoch 600 -0.56419355 [0.35324836]\n","Epoch 700 -0.58136296 [0.348402]\n","Epoch 800 -0.5886372 [0.34857824]\n","Epoch 900 -0.5638661 [0.36518708]\n","Epoch 0 1.2958211 [1.0094317]\n","Epoch 100 0.088235684 [0.60324466]\n","Epoch 200 -0.45029005 [0.3652865]\n","Epoch 300 -0.2994258 [0.34230822]\n","Epoch 400 -0.5860322 [0.3366996]\n","Epoch 500 -0.58539623 [0.34461787]\n","Epoch 600 -0.55100805 [0.3667983]\n","Epoch 700 -0.5656692 [0.36325985]\n","Epoch 800 -0.58064353 [0.35947326]\n","Epoch 900 -0.5865239 [0.36031032]\n","Epoch 0 0.75539696 [0.99830896]\n","Epoch 100 0.006698494 [0.56262666]\n","Epoch 200 -0.03544327 [0.6416413]\n","Epoch 300 0.035157967 [0.71265256]\n","Epoch 400 0.13412341 [0.8010901]\n","Epoch 500 -0.34133536 [0.34748867]\n","Epoch 600 -0.55445546 [0.3663635]\n","Epoch 700 -0.5603129 [0.36745822]\n","Epoch 800 -0.55271107 [0.37511882]\n","Epoch 900 -0.49131313 [0.41025913]\n","Epoch 0 0.8763678 [1.000829]\n","Epoch 100 -0.07834595 [0.53245044]\n","Epoch 200 -0.067596875 [0.63137364]\n","Epoch 300 0.060017623 [0.7406626]\n","Epoch 400 0.3416071 [0.8479867]\n","Epoch 500 -0.5868645 [0.35583678]\n","Epoch 600 -0.59944695 [0.35367653]\n","Epoch 700 -0.5020012 [0.40535894]\n","Epoch 800 -0.40679735 [0.4590654]\n","Epoch 900 -0.21641363 [0.5753162]\n","Epoch 0 0.9200596 [1.0017275]\n","Epoch 100 -0.04498514 [0.5421635]\n","Epoch 200 -0.01117979 [0.6590131]\n","Epoch 300 0.10486965 [0.7680697]\n","Epoch 400 0.5120032 [0.87590075]\n","Epoch 500 -0.4969323 [0.37959]\n","Epoch 600 -0.38475394 [0.44736347]\n","Epoch 700 -0.3543772 [0.46958783]\n","Epoch 800 -0.39101115 [0.45259726]\n","Epoch 900 -0.4167839 [0.44196954]\n","Epoch 0 1.2305686 [1.0078435]\n","Epoch 100 0.07133386 [0.5858553]\n","Epoch 200 0.033616733 [0.6760265]\n","Epoch 300 0.23305777 [0.8741287]\n","Epoch 400 -0.47255108 [0.3818614]\n","Epoch 500 -0.3758563 [0.44714132]\n","Epoch 600 -0.32301834 [0.48403075]\n","Epoch 700 -0.2562342 [0.5298705]\n","Epoch 800 -0.15931004 [0.5977943]\n","Epoch 900 0.08514862 [0.7878169]\n","Epoch 0 0.66721314 [0.9967645]\n","Epoch 100 -0.04353307 [0.54491234]\n","Epoch 200 -0.096022375 [0.60756373]\n","Epoch 300 -0.08967023 [0.628179]\n","Epoch 400 0.020504206 [0.7167625]\n","Epoch 500 0.20127441 [0.80883473]\n","Epoch 600 -0.6000891 [0.3477609]\n","Epoch 700 -0.5504448 [0.37678498]\n","Epoch 800 -0.47359937 [0.42044544]\n","Epoch 900 -0.46775532 [0.42738646]\n","Epoch 0 0.8971751 [1.0014476]\n","Epoch 100 0.05682884 [0.58954227]\n","Epoch 200 0.027133368 [0.69516516]\n","Epoch 300 0.07439848 [0.75082916]\n","Epoch 400 0.1924288 [0.83092105]\n","Epoch 500 -0.5501758 [0.3612658]\n","Epoch 600 -0.50957185 [0.38799778]\n","Epoch 700 -0.48669443 [0.40474364]\n","Epoch 800 -0.45023215 [0.428679]\n","Epoch 900 -0.41699317 [0.45111609]\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"14Zvx-vNrQcD","colab_type":"code","outputId":"490ad647-84bd-4b4e-8c44-491f3390458a","executionInfo":{"status":"ok","timestamp":1557263457117,"user_tz":-60,"elapsed":21398,"user":{"displayName":"Stratis Markou","photoUrl":"","userId":"09754366312766083286"}},"colab":{"base_uri":"https://localhost:8080/","height":550}},"source":["values, noises = [], []\n","for net in nets:\n","    values.append((net(torch.linspace(-5, 5, 200)[:, None].cuda()).cpu().data.numpy()* y_std) + y_mean)\n","    noises.append(net.log_noise.exp().cpu().data.numpy() * y_std)\n","      \n","values = np.array(values).reshape(no_nets, 200)\n","means, epistemic = values.mean(axis = 0), values.var(axis = 0)**0.5\n","noises = np.array(noises)\n","aleatoric = (noises**2).mean()**0.5\n","\n","total_unc = (aleatoric**2 + epistemic**2)**0.5\n","\n","c = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd',\n","     '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']\n","\n","plt.figure(figsize = (6, 5))\n","plt.style.use('default')\n","plt.scatter(x_train*x_std + x_mean, y_train*y_std + y_mean, s = 10, marker = 'x', color = 'black', alpha = 0.5)\n","plt.fill_between(np.linspace(-5, 5, 200)*x_std + x_mean, means + aleatoric, means + total_unc, color = c[0], alpha = 0.3, label = r\"$\\sigma(y'|x')$\")\n","plt.fill_between(np.linspace(-5, 5, 200)*x_std + x_mean, means - total_unc, means - aleatoric, color = c[0], alpha = 0.3)\n","plt.fill_between(np.linspace(-5, 5, 200)*x_std + x_mean, means - aleatoric, means + aleatoric, color = c[1], alpha = 0.4, label = r'$\\mathbb{E}_{q(\\mathbf{w})}[\\sigma^2]^{1/2}$')\n","plt.plot(np.linspace(-5, 5, 200)*x_std + x_mean, means, color = 'black', linewidth = 1)\n","plt.xlim([-5, 5])\n","plt.ylim([-5, 7])\n","plt.xlabel('$x$', fontsize=30)\n","plt.title('MAP Ensemble', fontsize=40)\n","plt.tick_params(labelsize=30)\n","plt.xticks(np.arange(-4, 5, 2))\n","plt.yticks(np.arange(-4, 7, 2))\n","plt.gca().yaxis.grid(alpha=0.3)\n","plt.gca().xaxis.grid(alpha=0.3)\n","plt.legend(loc = 2, fontsize = 22, frameon=False)\n","plt.savefig('map_homo.pdf', bbox_inches = 'tight')\n","\n","files.download(\"map_homo.pdf\")\n","\n","plt.show()"],"execution_count":19,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 600x500 with 1 Axes>"],"image/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"397.0625pt\" version=\"1.1\" viewBox=\"0 0 403.926562 397.0625\" width=\"403.926562pt\" 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